Question: Which of the following numbers is a multiple of 12? ${78,83,84,100,103}$
Explanation: The multiples of $12$ are $12$ $24$ $36$ $48$ ..... In general, any number that leaves no remainder when divided by $12$ is considered a multiple of $12$ We can start by dividing each of our answer choices by $12$ $78 \div 12 = 6\text{ R }6$ $83 \div 12 = 6\text{ R }11$ $84 \div 12 = 7$ $100 \div 12 = 8\text{ R }4$ $103 \div 12 = 8\text{ R }7$ The only answer choice that leaves no remainder after the division is $84$ $ 7$ $12$ $84$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $84$ $84 = 2\times2\times3\times7 12 = 2\times2\times3$ Therefore the only multiple of $12$ out of our choices is $84$. We can say that $84$ is divisible by $12$.